Math, asked by amir2632, 8 months ago

(2+y) (7-y)÷(5-y)(4+y)=1

Answers

Answered by siyasinhmar21

Answer:

3/2

Step-by-step explanation:

(2+y)(7-y)/(5-y)(4+y)=1

(2+y)(7-y)=(5-y)(4+y)

14-2y+7y-y^2=20+5y-4y-y^2

14+5y-y^2=20+y-y^2

-y^2+y^2+5y-y=20-14

4y=6

y=6/4

y=3/2

Answered by Anonymous

$<body bgcolor="white"><font color="midnightblue">$

$\huge\tt\purple{Answer:3/2}$ $\huge\tt\purple{or \: 1.5}$

$\bf\red{Step-by-Step}$ $\bf\red{Explanation:}$

$= (2 + y)(7 - y) \div (5 - y) \\ (4 + y) = 1$

$2(7 - y) + y(7 - y) \div 5(4 \\ + y) - y(4 + y) = 1$

$14 - 2y + 7y - {y}^{2} \div 20 \\ + 5y - 4y - {y}^{2} = 1$

$\frac{14 - 2y + 7y - {y}^{2} }{20 + 5y - 4y - {y}^{2} } = 1$

By cross multiplication,

$14 - 2y + 7y - {y}^{2} = 20 + \\ 5y - 4y - {y}^{2} = 1$

$- 2y + 7y - {y}^{2} - 5y + 4y + \\ {y}^{2} = 20 - 14$

+y2 will cancel with -y2.

$- 2y + 7y \cancel{ - {y}^{2} } - 5y + 4y \\ \cancel{ { + y}^{2} } = 6$

$5y - 5y + 4y = 6$

$4y = 6$

$y = \cancel{ \frac{6}{4} }$

$y = \frac{3}{2}$

$y = 1.5$

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